Question

Assuming the earth to be a sphere of uniform mass density. how much would it a body weight 800km below the surface of earth. if it's weight is 360 N on the surface given R= 6400 km.​

Answer 1

Question:-

Assuming the earth to be a sphere of uniform mass density. how much would it a body weight 800km below the surface of earth. if it's weight is 360 N on the surface given R= 6400 km.

Formula:-
`{g \tiny{f}} = (1 - (depth)/(radius))g`

Answer:-

We know:-

1. g = 10 m/s² on earth surface
2. R=6400 (Radius of earth)(given)
3. Weight on earth surface= 360N (given)
4. depth = 800 (given)

Solution:-

`{g \tiny{f}} = (1 - (depth)/(radius))g`

Putting the value of depth and Radius and g in formula .

`{g \tiny{f}} = (1 - (800)/(6400))10 \\{g \tiny{f}} = (1 - \frac{ \cancel{800}^( \: \: 1) }{{ \cancel{6400}}^( \: \: 2)} )10 \\ {g \tiny{f}} = (1 - (1)/(2) )10 \\ {g \tiny{f}} =( (2 - 1)/(2) )10 \\ {g \tiny{f}} = ( (1)/(2) ) * 10 \\ {g \tiny{f}} = 5 \: m {s}^( - 2)`

For mass :-

`weight = m * g \: (on \: surface) \\ 360 = m * 10 \\ 36 = m`

For weight at depth of 800 Km

`weight \: = m * g \\ w = 36 * 5 \\ w = 180 \: newton \: (N)`